Zozulya signed for the second division strugglers on loan from Real Betis last week but immediately came under fire from supporters who refused to accept his denial of the newspaper's allegation, which was later withdrawn.
Some Rayo fans voiced their disapproval of Zozulya's possible arrival during Sunday's 1-0 home win over Almeria, holding up pictures of the player wearing a Rayo jersey with the message "not welcome" and "our strip cannot be stained by racism".
"If the social atmosphere that breathes there, as we saw yesterday before the game, around the stadium and during the game, does not change, it's practically impossible that Roman can go there," Jose Lorenzo, one of the player's representatives, told reporters.
"It's not certain and tomorrow we will have a series of meetings and then a decision will be taken."
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Zozulya came under scrutiny when he arrived at Betis last year following his transfer from Dnipro Dnipropetrovsk after a Spanish newspaper reported incorrectly that he was wearing the shirt of a far-right paramilitary group.
The newspaper apologised and withdrew the article but after the player signed for Rayo, which has a large left-wing supporter base, on a six-month loan last week, the story resurfaced and fans staged protests at his first training session.
If Zozulya decides not to join Rayo he would be ineligible to play again this season as league rules state that players cannot register for more than two teams in one campaign.
(Reporting by Adriana Garcia, editing by Clare Fallon)
